Light-by-Light Scattering Constraint on Born-Infeld Theory

The recent measurement by ATLAS of light-by-light scattering in LHC Pb-Pb collisions is the first direct evidence for this basic process. We find that it excludes a range of the mass scale of a nonlinear Born-Infeld extension of QED that is $\lesssim 100\mathrm{GeV}$, a much stronger constraint than those derived previously. In the case of a Born-Infeld extension of the standard model in which the ${\mathrm{U}(1)}_Y$ hypercharge gauge symmetry is realized nonlinearly, the limit on the corresponding mass reach is $\sim 90\mathrm{GeV}$, which, in turn, imposes a lower limit of $\gtrsim 11\mathrm{TeV}$ on the magnetic monopole mass in such a ${\mathrm{U}(1)}_Y$ Born-Infeld theory.

Figure 1

Sketch of light-by-light scattering through photon-photon collisions in ultraperipheral Pb-Pb collisions.

Figure 2

Comparison between the angular distributions (with arbitrary normalizations) as functions of $\cos \theta$ in the center-of-mass frame (where $\theta$ is the polar angle) for the leading-order differential cross sections in $\mathrm{U}(1{)}_{\mathrm{EM}}$ Born-Infeld theory and QED, plotted as solid blue and dashed red lines, respectively.

Figure 3

The distributions in the scaled diphoton invariant mass $\tau \equiv m_{\gamma \gamma }^2/s_{NN}$, normalized by the total $\gamma \gamma \to \gamma \gamma$ cross section, for the QED case in the upper panel and for $\mathrm{U}(1{)}_{\mathrm{EM}}$ Born-Infeld theory with $M=\sqrt{\beta }=200\mathrm{GeV}$ in the lower panel.

Figure 4

The fiducial cross section for light-by-light scattering in relativistic heavy-ion collisions, $\sigma \mathbf{(}\mathrm{Pb}+\mathrm{Pb}(\gamma \gamma )\to {\mathrm{Pb}}^{(*)}+{\mathrm{Pb}}^{(*)}\gamma \gamma \mathbf{)}$ as a function of $M=\sqrt{\beta }$ in the $\mathrm{U}(1{)}_{\mathrm{EM}}$ Born-Infeld theory is shown as a solid green (blue) line for a hard cutoff (unitarized) approach, as discussed in the text. The lower diphoton invariant mass cutoff is set at 6 GeV (25 GeV) on the upper (lower) plot. This is compared with the 95% C.L. upper limit obtained from the ATLAS measurement [9] by combining the statistical and systematic errors in quadrature, as well as a 10 nb theoretical uncertainty in the cross section predicted in QED [8, 10] (the horizontal dashed line), which excludes the higher range shaded pink. The corresponding 95% C.L. lower limits $M\gtrsim 100(190)\mathrm{GeV}$ for $m_{\gamma \gamma }>6\mathrm{GeV}$ and $M\gtrsim 210(330)\mathrm{GeV}$ for $m_{\gamma \gamma }>25\mathrm{GeV}$ are shown as vertical dashed lines in green (blue).